Shivam has two grandsons Rupesh and Mandar. 12 year old Rupesh gets some money from Shivam’s wealth and 13 year old Mandar gets rest of the money. But Rupesh and Mandar will get money only when they turn 23 years old. Till then the money is in a bank getting interest at rate 8% compounded annually. When both turn 23, they receive the same amount. How much had Shivam given Mandar (in Rs.) initially, if total money with Shivam was Rs. 24700?

Correct option is D

Given:

Total money with Shivam = Rs. 24700

Rupesh is 12 years old, Mandar is 13 years old

Interest rate = 8% compounded annually

Both receive the same amount when they turn 23 years old

The money is given to both Rupesh and Mandar until they turn 23.

Formula Used:

Compound Interest formula:

A = $$P \left(1 + \frac{r}{100}\right)^t$$​​

Where:

A = Amount after time t, P = Principal (initial money)

r = Interest rate, t = Time in years

Solution: 

Let Rupesh gets x and Mandar get y amount.

Since both receive the same amount after they turn 23 year old.

So,

​$$x \left(1 + \frac{8}{100}\right)^{11} = y \left(1 + \frac{8}{100}\right)^{10} \\ \ \\ \implies \frac{x}{y} = \frac{100}{108} = \frac{25}{27}$$​​

Now, let x = 25k, and y = 27k 

So, 

25k + 27k = 24700

52k = 24700 

k =$$\frac{24700}{52}$$​ = 475 

Mandar gets = 27k = 27 × 475 = Rs. 12825

Thus, the initial amount given to Mandar is Rs. 12825